Mathematical modelling of avascular tumour growth based on diffusion of nutrients and its validation
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Bibliographic record
Abstract
Abstract In this paper, a mathematical model based on the diffusion of nutrients is developed by considering the physiological changes accompanying the growth of avascular tumour. Avascular tumour growth involves the formation of three different zones namely proliferation, quiescent and necrotic zones. The main processes on which avascular tumour growth depends are: (i) diffusion of nutrients through the tumour from the contiguous tissues, (ii) consumption rate of the nutrients by the cells in the tumour, and (iii) cell death by apoptosis and necrosis. In the model, we consider the tumour to be spherical and the principal nutrients responsible for its growth are oxygen and glucose. By solving for the concentration profiles using the model developed, we are able to compute the radii of the quiescent and necrotic zones as well as that of the tumour. The proposed model is also validated using in vitro tumour growth data and Gompertzian empirical relationship parameters available in the literature. Our model is also successful in capturing the saturated volume of the avascular tumour for different nutrient concentrations at the tumour surface.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it